The difference between spatial and intrinsic parity

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Discussion Overview

The discussion revolves around the concepts of spatial and intrinsic parity in quantum mechanics, specifically at a level comparable to Griffiths' textbook. Participants seek to clarify the definitions and distinctions between these two types of parity, as well as their implications for different types of particles.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant requests definitions for spatial and intrinsic parity, noting confusion due to inconsistent usage in various sources.
  • Another participant explains that the parity of a particle is the product of intrinsic and extrinsic (spatial) parity, with extrinsic parity defined as ##(-1)^l##, where ##l## is the orbital angular momentum.
  • A participant seeks clarification on whether intrinsic parity is the eigenvalue of the operator that inverts the signs in the position wavefunction and questions how extrinsic parity relates to this operator.
  • It is noted that a single fundamental particle has intrinsic parity, while composite particles may have both intrinsic and extrinsic parity, depending on their configuration and constituents.
  • One participant mentions that the sign associated with parity is a matter of convention.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and relationships between spatial and intrinsic parity, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Some assumptions regarding the definitions of parity and the implications of particle composition may be missing, and the relationship between intrinsic and extrinsic parity is not fully clarified.

Coffee_
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Can someone explain on the level of Griffiths QM what the difference between those two parities since I'm quite confused here. Some sources use the terms interchangably, some don't.

Could anyone provide good definitions for both terms?

Spatial parity seems pretty obvious to me to be the eigenvalue associated with an eigenstate of the position vector inversion.
 
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In general the parity of a particle is the product of intrinsic and extrinsic (or spatial as you say) parity. Extrinsic parity is given by ##(-1)^l## where ##l## is the orbital angular momentum of the state. Intrinsic parity is peculiar of each particle and it simply says as the state of the particle change under a parity transformation:
$$
P\vert \pi\rangle=\vert \pi\rangle\quad\text{for positive parity}
$$
$$
P\vert \pi\rangle=-\vert \pi\rangle\quad\text{for negative parity}
$$
 
Firs off, thanks for the answer.

Right,so the intrinsic parity is the eigenvalue of the operator that switches all the signs in the position wavefunction?

How does extrinsic parity relate to this operator and eigenvalue?
 
a single fundamental particle (like a single quark) will have intrinsic parity.
a composite or a group of particle(s) will have intrinsic parity (due to the constituents/members) + maybe extrinsic parity (due to the configuration of those particles).
The sign is just a matter of convention.
 

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